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arlik [135]
3 years ago
10

How many 1/5 liter glasses can Lin fill with a 1 1/2 liter bottle of water?

Mathematics
1 answer:
RoseWind [281]3 years ago
8 0

Answer:

The number of 1/5 liter glasses that Lin can fill is 7\frac{1}{2}

Step-by-step explanation:

we know that

To find out how many 1/5 liter glasses can Lin fill with a 1 1/2 liter bottle of water, divided 1 1/2 by 1/5

so

1\frac{1}{2} :\frac{1}{5}

Convert mixed number to an improper fraction

1\frac{1}{2}=1+\frac{1}{2}=1\frac{1*2+1}{2}=\frac{3}{2}

substitute

\frac{3}{2} :\frac{1}{5}

Multiply in cross

\frac{5*3}{2*1}=\frac{15}{2}=7.5

Convert to mixed number

7.5=7+\frac{1}{2}=7\frac{1}{2}

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Answer:

1. Rewriting the expression 5.a.b.b.5.c.a.b.5.b using exponents we get: \mathbf{5^3a^2b^4c}

5.  x^-6 = \frac{1}{x^6}

6. 5^{-3}.3^{-1}=\frac{1}{5^3.3^1}

7. a^{-3}b^0c^4=\frac{c^4}{a^3}

Step-by-step explanation:

Question 1:

We need to rewrite the expression using exponents

5.a.b.b.5.c.a.b.5.b

We will first combine the like terms

5.5.5.a.a.b.b.b.b.c

Now, if we have 5.5.5 we can write it in exponent as: =5^{1+1+1}=5^3

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b.b.b.b as: b^{1+1+1+1}=b^4

So, our result will be:

5^3a^2b^4c

Rewriting the expression 5.a.b.b.5.c.a.b.5.b using exponents we get: \mathbf{5^3a^2b^4c}

Question:

Rewrite using positive exponent:

The rule used here will be: a^{-1}=\frac{1}{a^1} which states that if we need to make exponent positive, we will take it to the denominator.

Applying thee above rule for getting the answers:

5) x^{-6} = \frac{1}{x^6}

6) 5^{-3}.3^{-1}=\frac{1}{5^3.3^1}

7) a^{-3}b^0c^4=\frac{b^0c^4}{a^3}

We know that b^0=1 so, we get

a^{-3}b^0c^4=\frac{b^0c^4}{a^3}=\frac{c^4}{a^3}

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